基于并行Kleinman 迭代算法的Markov 跳变系统优化??∞ 控制

基于Kleinman 迭代算法的框架, 提出两种数值迭代算法, 用于解决连续时间Markov 跳变系统的优化??_∞ 控制器设计问题. 首先, 给出“ 直接并行Kleinman 迭代算法”, 并从正实算子的收敛性证明该算法的收敛性; 然后, 基于直接并行Kleinman 迭代算法, 提出一种更加广义的迭代算法结构, 即“ 广义并行Kleinman 迭代算法”, 并论述其包含的4 种情形; 最后, 通过数值示例验证了所提出算法的有效性.

Optimal ??∞ control of Markov jump systems based on parallel Kleinman iteration algorithm

Based on the framework of Kleinman iteration algorithm, two computation iteration algorithms are studied to solve the optimal ??_∞ control problems for continuous-time Markov jump linear systems. Firstly, the direct parallel Kleinman iteration algorithm is proposed and the proof of the convergence of the iterative algorithm is established. Then, based on the direct parallel Kleinman, a more general iterative algorithm, called generalized parallel Kleinman iteration algorithm, is proposed with four different cases. Finally, a numerical example is provided to illustrate the effectiveness of the proposed algorithms.